US8718985B2 - Method for establishing machine code, the execution of which generates an optimized rolling model - Google Patents

Method for establishing machine code, the execution of which generates an optimized rolling model Download PDF

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US8718985B2
US8718985B2 US12/999,773 US99977309A US8718985B2 US 8718985 B2 US8718985 B2 US 8718985B2 US 99977309 A US99977309 A US 99977309A US 8718985 B2 US8718985 B2 US 8718985B2
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rolling
model
rolling stock
mathematical functions
condition
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US20110106512A1 (en
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Marc Hainke
Matthias Kurz
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Siemens AG
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Siemens AG
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B17/00—Systems involving the use of models or simulators of said systems
    • G05B17/02—Systems involving the use of models or simulators of said systems electric
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
    • G05B13/048—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators using a predictor
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B21—MECHANICAL METAL-WORKING WITHOUT ESSENTIALLY REMOVING MATERIAL; PUNCHING METAL
    • B21B—ROLLING OF METAL
    • B21B37/00—Control devices or methods specially adapted for metal-rolling mills or the work produced thereby
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B2219/00—Program-control systems
    • G05B2219/30—Nc systems
    • G05B2219/35—Nc in input of data, input till input file format
    • G05B2219/35017—Finite elements analysis, finite elements method FEM

Definitions

  • the present invention relates to a method for establishing machine code which can be executed directly by a computer and the execution of which by the computer causes the computer to implement a rolling model and to determine an output variable which quantitatively describes at least one material flow occurring in the rolling stock during a rolling process defined by the condition of the rolling stock and the stand setting, said output variable being determined on the basis of the rolling model, a condition of rolling stock lying within a predetermined range of conditions and a stand setting lying within a predetermined range of settings.
  • the present invention also relates to a computer program having machine code which can be executed directly by a computer and the execution of which by the computer causes the computer to implement such a rolling model and to determine the output variable on the basis of the rolling model, the condition of the rolling stock and the stand setting.
  • the present invention also relates to a data storage medium which stores such a computer program in machine-readable form.
  • the present invention also relates to a computer which is programmed using such a computer program, such that the computer executes the computer program during operation.
  • the present invention relates to a rolling mill train having at least one rolling stand and a computer in the form of a control device for a rolling mill train, the computer executing the computer program online in conjunction with the control of the rolling mill train, and the at least one rolling stand being controlled by the computer.
  • both the so-called dog-boning which occurs during edging passes and the so-called bulging and constriction which occur during flat passes can be modeled and quantitatively predicted, in particular.
  • the profile and flatness of the strip-shaped rolling stock can also be predicted with a good degree of accuracy in the case of a sequence of flat passes.
  • Finite element methods operate with a high resolution. With computer powers which are possible nowadays, several hours are needed for the prediction. These models are not suitable for online calculations which may last only a few seconds. Empirical models are therefore used during online calculations. However, in the case of strip-shaped rolling stock for example, the empirical models are unsuitable for providing accurate statements relating to the strip form, the strip profile and the strip flatness.
  • a method for establishing machine code which can be executed directly by a computer and the execution of which by the computer causes the computer to implement a rolling model based on mathematical/physical equations and to determine an output variable which quantitatively describes at least one material flow occurring in the rolling stock during a rolling process defined by the condition of the rolling stock and the stand setting, said output variable being determined on the basis of the rolling model, a condition of the rolling stock lying within a predetermined range of conditions and a stand setting lying within a predetermined range of settings,
  • the analysis of all of the output conditions determined can be a singular value decomposition.
  • a quadratic, symmetrical matrix can be determined on the basis of all of the output conditions determined, and the adapted formulation functions may correspond to some of the eigenvectors of the quadratic, symmetrical matrix.
  • the eigenvalues of the quadratic, symmetrical matrix can be determined, and the adapted formulation functions may correspond to the eigenvectors associated with the largest eigenvalues.
  • the rolling model may have an advance block and a main block, the condition can be transformed into components of the adapted formulation functions in the advance block, and the output variable can be determined in the main block on the basis of the components of the adapted formulation functions and the stand settings.
  • the output variable may comprise a number of weighting factors which each specify the extent to which a respective corresponding formulation function of the adapted formulation functions occurs in the rolling stock following the rolling process defined by the condition of the rolling stock and the stand setting.
  • the basic model can be established during the establishing method.
  • the rolling stock can be strip-shaped rolling stock.
  • the rolling model quantitatively may describe the material flow occurring when calibration rolls of an edger are used.
  • a computer program may have machine code obtained by an establishing method as described above.
  • a data storage medium may store a computer program as described above in machine-readable form.
  • a computer may be programmed using a computer program as described above, such that the computer executes the computer program during operation.
  • the computer can be in the form of a control device for a rolling mill train and executes the computer program online in conjunction with the control of the rolling mill train.
  • a rolling mill train may have at least one rolling stand and a computer as described above, wherein the at least one rolling stand being controlled by the computer.
  • FIG. 1 diagrammatically shows a rolling mill train
  • FIG. 2 shows a flowchart
  • FIG. 3 shows the method of operation of the rolling model
  • FIGS. 4 to 6 show possible cross sections of strip-shaped rolling stock
  • FIG. 7 shows a flowchart
  • FIG. 8 shows a block diagram for additionally explaining FIG. 7 .
  • FIGS. 9 and 10 show flowcharts
  • FIG. 11 shows a block diagram
  • a number of basic conditions of the rolling stock lying within the desired range of conditions and a number of basic stand settings lying within the range of settings are predefined for a basic model which is based on mathematical/physical equations and uses universal formulation functions.
  • An output condition is respectively determined using the basic model.
  • Each output condition is described by a number of weighting factors which each specify the extent to which a respective corresponding formulation function of the universal formulation functions occurs in the rolling stock following the rolling process defined by the respective basic condition of the rolling stock and the respective basic stand setting.
  • Adapted formulation functions are determined by analyzing all of the output conditions determined.
  • the number of adapted formulation functions is considerably smaller than the number of universal formulation functions.
  • the rolling model is established using the adapted formulation functions, the rolling model being based on the mathematical/physical equations.
  • the machine code is established on the basis of the rolling model.
  • a quadratic matrix is determined on the basis of all of the output conditions determined, and the adapted formulation functions correspond to some of the eigenvectors of the quadratic matrix.
  • the weighting factors of each output condition may be written as a column vector, for example, and the individual column vectors may be written beside one another. This results in a coefficient matrix.
  • the coefficient matrix is multiplied by its transpose.
  • the matrix product produces a quadratic, symmetrical matrix whose eigenvectors can then be determined.
  • the adapted formulation functions correspond to the eigenvectors associated with the largest eigenvalues.
  • the eigenvalues can be sorted according to size (the largest first, the smallest last).
  • the first n eigenvalues for example, can be singled out, for example 5, 10 or 15 eigenvalues.
  • the first x percent of the eigenvalues can also be
  • All eigenvalues which are larger than a threshold value can also be singled out.
  • the threshold value may alternatively be stated as an absolute value or as a fraction of the largest eigenvalue.
  • the rolling model it is possible to establish the rolling model in such a manner that the condition is predefined to the rolling model already on the basis of the adapted formulation functions.
  • the rolling model it is possible for the rolling model to have an advance block and a main block, for the condition to be transformed into components of the adapted formulation functions in the advance block, and for the output variable to be determined in the main block on the basis of the components of the adapted formulation functions and the stand settings. It goes without saying that the rolling model is accordingly determined during the establishing method in this case.
  • the output variable preferably comprises a number of weighting factors which each specify the extent to which a respective corresponding formulation function of the adapted formulation functions occurs in the rolling stock following the rolling process defined by the condition of the rolling stock and the stand setting.
  • the basic model may be given. It may alternatively be established during the establishing method.
  • the rolling stock may be of any desired nature. It may be strip-shaped rolling stock, for example.
  • the rolling model in particular, may quantitatively describe the material flow occurring when calibration rolls of an edger are used.
  • Yet other embodiments also relate to a data storage medium which stores such a computer program in machine-readable form.
  • Yet other embodiments also relate to a computer which is programmed using such a computer program, such that the computer executes the computer program during operation.
  • the computer It is possible for the computer to operate offline, that is to say in a manner detached from the control of a rolling mill train.
  • the rolling model requires only very little computational complexity on account of the use of the adapted formulation functions. It is therefore fast enough for the computer to be in the form of a control device for a rolling mill train and to execute the computer program online in conjunction with the control of the rolling mill train.
  • other embodiments also relate to a rolling mill train having at least one rolling stand and such a computer, the at least one rolling stand being controlled by the computer.
  • a rolling mill train for rolling rolling stock 1 has a number of rolling stands 2 , 3 .
  • the rolling stock 1 is strip-shaped rolling stock 1 in this case.
  • various embodiments can also be used for other types of rolling stock 1 , for example for rod-shaped or tubular rolling stock 1 .
  • the strip-shaped rolling stock 1 can be rolled in flat passes using at least some of the rolling stands 2 , 3 —the rolling stands 2 in this case.
  • the rolling stands 2 which can be used to roll the strip-shaped rolling stock 1 in flat passes must be present.
  • edgers 3 the rolling stands 3 in this case—in which the strip-shaped rolling stock 1 is subjected to edging passes may also be present.
  • the edgers 3 may have calibration rolls for this purpose.
  • the edgers 3 are not present in all rolling mill trains. They are depicted only using dashed lines in FIG. 1 for this reason.
  • the rolling mill train also has a computer 4 which controls the rolling stands 2 , 3 and also the rolling mill train as a whole. According to FIG. 1 , the computer 4 is therefore in the form of a control device for the rolling mill train.
  • the computer 4 is programmed using a computer program 5 .
  • the computer program 5 may have been supplied to the computer 4 via a computer-computer link 6 (LAN, World Wide Web, etc.), for example.
  • LAN Local Area Network
  • World Wide Web etc.
  • the computer program 5 it is possible for the computer program 5 to be stored on a data storage medium 7 in machine-readable form and to then be supplied to the computer 4 via the data storage medium 7 .
  • a CD-ROM is illustrated as the data storage medium 7 in FIG. 1 .
  • the data storage medium 7 may alternatively have a different design, for example as a USB memory stick or an SD memory card.
  • the computer program 5 has machine code 8 .
  • the machine code 8 can be directly and immediately executed by the computer 4 . It is executed by the computer 4 during operation. Operation of the computer 4 is explained briefly below in connection with FIG. 2 .
  • the computer 4 first of all implements a rolling model 9 (additionally see FIG. 3 ) in a step S 1 .
  • the computer 4 receives a condition Z of the strip-shaped rolling stock 1 and a desired output condition Z* of the
  • the condition Z relates to the condition of the strip-shaped rolling stock 1 before rolling and the desired output condition Z* relates to the condition of the strip-shaped rolling stock 1 following the rolling process. At least the condition Z lies within a predetermined range of conditions.
  • the desired output condition Z* preferably also lies within the desired range of conditions.
  • a step S 3 the computer 4 determines a preliminary stand setting G.
  • the stand setting G lies within a predetermined range of settings for a modeled rolling stand 2 , 3 .
  • the stand setting G may define, for example, whether a flat pass or an edging pass is involved and how the rolling stand 2 , 3 which carries out the pass has been set.
  • a step S 4 the computer 4 determines an output variable A on the basis of the rolling model 9 , the condition Z and the stand setting G.
  • the rolling model 9 therefore provides the output variable A on the basis of the condition Z predefined to it and the stand setting G predefined to it.
  • the output variable A generally has a number of weighting factors a which specify the extent to which an adapted formulation function ⁇ associated with the respective weighting factor a occurs in the strip-shaped rolling stock 1 following the rolling process (as defined by the respective condition Z of the strip-shaped rolling stock 1 and the respective stand setting G).
  • the weighting factors a can be determined, for example, with the aid of the Galerkin method which is generally known to experts. Alternatively, the weighting factors a can be determined using a variation formulation, for example.
  • an index i is additionally used in FIG. 3 (and also at other points) in order to indicate that a plurality of respectively different adapted formulation functions p, weighting factors a etc. are involved.
  • the output variable A quantitatively describes at least one material flow occurring in the strip-shaped rolling stock 1 during a rolling process defined by the condition Z and the stand setting G. If appropriate, the output variable A may describe other properties. However, at least the abovementioned property is quantitatively described.
  • step S 5 the computer 4 checks whether the output variable A determined corresponds to the desired output condition Z* (within permissible tolerances). If this is not the case, the computer 4 moves to a step S 6 in which it varies the stand setting G within the range of settings. From step S 6 , the computer 4 returns to step S 4 .
  • step S 7 the computer 4 drives the corresponding rolling stand 2 , 3 in accordance with the stand setting G determined last.
  • Steps S 2 to S 7 are run through repeatedly on the basis of a step S 8 until the method in FIG. 2 is intended to be terminated.
  • step S 7 may be replaced, for example, with a step (not illustrated) in which the respectively determined output variable A is stored or is output to a user of the computer 4 .
  • the rolling model 9 is designed according to FIG. 3 in such a manner that it is based on mathematical/physical equations.
  • the mathematical/physical equations may comprise algebraic equations.
  • the mathematical/physical equations may comprise (partial) differential equations according to FIG. 3 .
  • adapted formulation functions ⁇ that is to say formulation functions ⁇ which are tailored to the typical passes of the respective rolling stand(s) 2 , 3 , are used in the rolling model 9 according to FIG. 3 .
  • the material flow comprises at least the transverse flow transverse to the rolling direction x of the strip-shaped rolling stock 1 , that is to say in the width direction of the strip-shaped rolling stock 1 .
  • the material flow preferably also comprises the longitudinal flow in the rolling direction x.
  • the profile and/or the flatness of the strip-shaped rolling stock 1 can be determined using the rolling model 9 .
  • the output variables A of the rolling model 9 quantitatively describe both so-called dog-boning (see FIG. 4 ) and bulging (see FIG. 5 ) and constriction (see FIG. 6 ) of the strip-shaped rolling stock 1 .
  • the so-called dog bone can occur in edging passes and bulging and constriction can occur in flat passes.
  • the manner in which the rolling model 9 is established is arbitrary in principle.
  • the decisive factor is that the rolling model 9 is based on the adapted formulation functions T. For this reason, the model has online capabilities despite the use of the mathematical/physical equations.
  • a basic model 9 ′ is first of all established in a step S 11 .
  • the basic model 9 ′ is based on the same mathematical/physical equations as the rolling model 9 .
  • the difference from the rolling model 9 is that universal formulation functions ⁇ ′, that is to say formulation functions ⁇ ′ which are not specifically tailored to the description of particular rolling processes, are used to establish the basic model 9 ′.
  • the universal formulation functions ⁇ ′ may be based on the finite element method. A large number of universal formulation functions ⁇ ′ (typically several thousand, in some cases more than 10,000) are needed to establish the basic model 9 ′.
  • the basic model 9 ′ need not necessarily be established during the establishing method according to various embodiments. It may be alternatively given in other ways. Suitable basic models 9 ′ are even commercially available in some cases.
  • a basic condition Z′ of the strip-shaped rolling stock 1 is predefined to the basic model 9 ′. Furthermore, a basic stand setting G′ is predefined to the basic model 9 ′ during step S 12 .
  • the basic condition Z′ lies within the predetermined range of conditions.
  • the basic stand setting G′ lies within the predetermined range of settings.
  • an output condition A′ is respectively determined using the basic model 9 ′.
  • the output condition A′ is described by a number of weighting factors a′ according to FIG. 8 .
  • the weighting factors a′ each specify the extent to which a universal formulation function ⁇ ′ associated with the respective weighting factor a′ occurs in the strip-shaped rolling stock 1 following the rolling process (as defined by the basic condition Z′ and the stand setting G′).
  • the output condition A′ determined is stored in step S 13 .
  • the weighting factors a′ may be determined in a similar manner to the weighting factors a. The difference is that the weighting factors a′ are based on the universal formulation functions ⁇ ′ and the weighting factors a are based on the adapted formulation functions ⁇ .
  • step S 14 is check is carried out in order to determine whether the determination of output conditions A′ is intended to be terminated. If this is not the case, the method returns to step S 12 . Otherwise, the establishing method is continued with a step S 15 .
  • step S 15 all of the output conditions A′ determined are analyzed.
  • the adapted formulation functions ⁇ are then determined in a step S 16 on the basis of the analysis in step S 15 .
  • the number of adapted formulation functions ⁇ is considerably smaller than the number of universal formulation functions ⁇ ′. It is generally far less than 100, for example less than 70, in some cases even less than 50.
  • the rolling model 9 is established in a step S 17 .
  • the rolling model 9 is established using the adapted formulation functions ⁇ determined in step S 16 .
  • a step S 18 the rolling model 9 is used to establish the machine code 8 which can be executed directly by the computer 4 and the execution of which gives rise to the above-described method of operation of the computer 4 .
  • the machine code 8 which corresponds, in its entirety, to the computer program 5 is then stored, for example on the data storage medium 7 .
  • steps S 15 and S 16 in FIG. 7 it is possible, for example, according to FIG. 9 to first of all carry out a singular value decomposition of all of the output conditions A′ determined in a step S 21 and to then select the singular values which occur most in a step S 22 .
  • the number of singular values selected is considerably smaller than the number of universal formulation functions ⁇ ′ (typically at most 100 in comparison with several thousand).
  • An associated adapted formulation function ⁇ is then determined for each singular value in a step S 23 .
  • a matrix M is first of all established in a step S 31 .
  • the weighting factors a′ of each output condition A′ determined may each form a column of the matrix M.
  • the output conditions A′ may be set as the columns of the matrix M as they are.
  • the matrix determined in this manner referred to as the condition matrix below—does not yet constitute the matrix M. This is because the mean value of the respective row is preferably determined for each row in the condition matrix. The mean value is then subtracted from the matrix elements in the respective row.
  • the matrix which has been determined in this manner and has been modified row by row forms the matrix M established in step S 31 .
  • a step S 32 the matrix M is multiplied by its transpose M T .
  • the matrix product determined in this manner produces a quadratic, symmetrical matrix Q.
  • a step S 33 the eigenvalues of the quadratic, symmetrical matrix Q are determined.
  • a step S 34 the eigenvalues of the quadratic, symmetrical matrix Q are determined.
  • the limit to which the eigenvalues are selected may be predefined in different ways. For example, it is possible to predefine an absolute number of eigenvalues. Alternatively, it is possible to predefine a percentage of the eigenvalues. It is likewise possible to predefine an absolute value and to select all eigenvalues which are greater than or greater than/equal to this value. It is also possible to divide all eigenvalues by the highest eigenvalue and to select all eigenvalues in which the quotient with the largest eigenvalue is greater then or greater than/equal to a predetermined limit.
  • step S 35 the eigenvectors which correspond to the eigenvalues selected in step S 34 are determined.
  • step S 36 the corresponding adapted formulation functions ⁇ are determined on the basis of the eigenvectors of the quadratic matrix Q. If, in accordance with the preferred procedure, the mean values are subtracted from the matrix elements during step S 31 , the mean values are added to the individual components of the eigenvectors in step S 36 .
  • the rolling model 9 operates with the adapted formulation functions ⁇ .
  • the condition Z in an appropriately adapted form during the steps in FIG. 2 or in the illustration in FIG. 3 .
  • the rolling model 9 it is possible for the rolling model 9 to have an advance block 10 and a main block 11 .
  • the condition Z is transformed into components k of the adapted formulation functions ⁇ in the advance block 10 .
  • the output variable A is determined in the main block 11 on the basis of the components k of the adapted formulation functions ⁇ and the stand settings G.
  • the rolling model 9 is accordingly established during the procedure in FIGS. 7 to 10 in this case.
  • the various embodiments have many advantages.
  • the quality of the rolling model 9 is almost as high as that of the basic model 9 ′ (which is typically based on the finite element method).
  • the computational complexity for determining the output variable A is drastically reduced since—

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DE102008030243.0 2008-06-25
DE102008030243 2008-06-25
DE102008030243A DE102008030243A1 (de) 2008-06-25 2008-06-25 Erstellverfahren für ein optimiertes Walzmodell
PCT/EP2009/056236 WO2009156234A2 (de) 2008-06-25 2009-05-22 Erstellverfahren für maschinencode, dessen ausführung ein optimiertes walzmodell realisiert

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EP (1) EP2303483B1 (de)
CN (1) CN102076438B (de)
BR (1) BRPI0914661A2 (de)
DE (1) DE102008030243A1 (de)
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DE102008030243A1 (de) 2008-06-25 2009-12-31 Siemens Aktiengesellschaft Erstellverfahren für ein optimiertes Walzmodell
EP2527053A1 (de) * 2011-05-24 2012-11-28 Siemens Aktiengesellschaft Steuerverfahren für eine Walzstraße
EP2527054A1 (de) * 2011-05-24 2012-11-28 Siemens Aktiengesellschaft Steuerverfahren für eine Walzstraße
CN110520805B (zh) * 2017-04-18 2022-12-06 首要金属科技德国有限责任公司 过程模型的建模优化
CN110434172B (zh) * 2019-07-16 2020-05-08 北京科技大学 一种炉卷和精轧机组连轧的负荷分配计算方法
EP3798750B1 (de) * 2019-09-25 2024-09-25 SMS group GmbH Verfahren zum überwachen und steuern einer anlage zum walzen metallener produkte
CN110947774B (zh) * 2019-12-06 2020-12-01 东北大学 一种考虑轧制宽展的板形预测方法
EP4124398B1 (de) * 2021-07-27 2024-04-10 Primetals Technologies Austria GmbH Verfahren zur bestimmung mechanischer eigenschaften eines walzgutes mit hilfe eines hybriden modells

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DE102008030243A1 (de) 2009-12-31
CN102076438A (zh) 2011-05-25
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CN102076438B (zh) 2014-07-23
BRPI0914661A2 (pt) 2015-10-20
EP2303483B1 (de) 2016-05-11
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US20110106512A1 (en) 2011-05-05
EP2303483A2 (de) 2011-04-06

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